Hi Kari
I found the following useful information regarding marriage in Honduras:
If you are NOT a Honduran citizen, you will be required the following documents:

A valid passport
A certified copy of your birth certificate (1)
A certified copy of your police record (2)
An Affidavit of Single Status (3)
You will need two witnesses to your wedding - non-relatives preferred. They must have the following documents:
For non-Honduran citizens: A valid passport for at least six months
For Honduran citizens: A Honduran Identity card ("Cédula de Identidad")
Marriages legally performed and valid in Honduras are also legally valid in other countries. Your marriage will be legally recognized in the U.S. when you or your lawyer who performed the ceremony submits your marriage certificate with the appropriate certifications to the U.S. Embassy in Honduras.

I was unable to find any information on waiting periods for marriages in Honduras, or Central America for that matter, but I suggest you call either the American Embassy in Honduras or the Honduran Embassy in Washington DC to find out more about this.

Embassy of Honduras, Washington DC, United States: +1 202 966 7702
American Embassy, Tegucigalpa, Honduras: +504 236 9320

I hope this helps!